Spectral analysis of mathematical models in quantum field theory
Final Report Abstract
In recent years, powerful methods have been developed for the rigorous treatment of mathematical models in semi-relativistic quantum electrodynamics. In the present project, we aimed at extending and developing the high potential of these methods in order to provide a mathematically rigorous study of processes in fully relativistic quantum field theory beyond quantum electrodynamics. As an example of such a process from a different sector of the Standard model, we studied the spectral theory of the decay of the negatively charged intermediate vector boson of the weak nuclear interaction into an electron and a massless electron antineutrino. Under general assumptions, covering, in particular, the physically relevant case, we proved that the spectrum of the corresponding interacting Hamiltonian extracted from the Standard Model is purely absolutely continuous between the ground state energy and the first threshold given by the electron mass. Since the strategy of the proof is very robust, a wide range of mathematical models in quantum field theory at low energy comes within reach. Better yet, this strategy, in an even simpler form, also allows to derive the pure absolute continuity of the spectrum at arbitrary energies strictly between consecutive thresholds. However, in the vicinity of the thresholds, this strategy breaks down, leaving a rich set of interesting open problems to be tackled in the future.
Publications
- 2011 Spectral theory for a mathematical model of the weak interactions: The decay of the intermediate vector bosons W ± , II. Ann. Henri Poincaré 12 1539–70
Aschbacher W H, Barbaroux J-M, Faupin J, and Guillot J-C
